Cycles in \(k\)-traceable oriented graphs (Q641171)

A digraph of order at least \(k\) is said to be \(k\)-traceable if each of its sub-digraphs of order \(k\) is traceable. The paper presents some results pertaining to various cycle properties of strong \(k\)-traceable oriented graphs and investigates the extent to which pancyclicity is retained by strong \(k\)-traceable oriented graphs. In addition, it establishes an upper bound on the order of \(k\)-traceable oriented graphs having a strong component with girth greater than 3. It is also shown that the Path Partition Conjecture holds for 1-deficient oriented graphs having a strong component with girth at least 6.